find thae area of a circle inscribed in a square whose diagonal is 8 feet long

Question

Please asnwer the question

Answer 1

Hi Carmelo,

 

Let the radius of the circle be r.

A right triangle with vertices at the center of the circle, at the midpoint of one of the sides and at one of the vertices of the square can be formed. This will indeed be an isosceles right triangle with sides equal to r. The hypotenuse will be half of the diagonal length. Then, using the Pythagorean Theorem, we can write

r^2 + r^2 = 4^2

2r^2 = 16

r^2 = 8 

Stop here! We don't need to find r. We are interested in finding the area of the circle and since the area of a circle is pi*r^2, r^2 is what we really need.

Let the area of the circle be S.

S = 3.14*8

= 25.12 ft^2 (approximately)